Related papers: Equivalence Problem for Second Order Partially Dif…
In this paper we study the Neumann problem for a type of fully nonlinear second order elliptic partial differential equations on domains in $\mathbb{C}^{n}$ without any curvature assumptions on the domain.
This article is focused on two related topics within the study of partial differential equations (PDEs) that illustrate a beautiful connection between dynamics, topology, and analysis: stability and spatial dynamics. The first is a property…
Partial differential equations (PDEs) are typically used as models of physical processes but are also of great interest in PDE-based image processing. However, when it comes to their use in imaging, conventional numerical methods for…
We consider a specific type of nonlinear partial differential equations (PDE) that appear in mathematical finance as the result of solving some optimization problems. We review some existing in the literature examples of such problems, and…
We study fully nonlinear second-order (forward) stochastic partial differential equations (SPDEs). They can also be viewed as forward path-dependent PDEs (PPDEs) and will be treated as rough PDEs (RPDEs) under a unified framework. We…
We prove duality estimates for time-fractional and more general subdiffusion problems. An important example is given by subdiffusive porous medium type equations. Our estimates can be used to prove uniqueness of weak solutions to such…
High-dimensional partial differential equations (PDE) appear in a number of models from the financial industry, such as in derivative pricing models, credit valuation adjustment (CVA) models, or portfolio optimization models. The PDEs in…
We prove a few cases of a conjecture on the invariance of cohomological support loci under derived equivalence by establishing a concrete connection with the related problem of the invariance of Hodge numbers. We use the main case in order…
In this work we propose a mechanism for converting the spectral problem of vertex models transfer matrices into the solution of certain linear partial differential equations. This mechanism is illustrated for the…
Heuristic arguments and order of magnitude estimates for partial differential equations highlight essential features of the physics they describe. We present order of magnitude estimates, and their limitations, for the three classic second…
In this paper we will consider two curl-curl equation in two dimensions. One curl-curl problem for a scalar quantity $F$ and one problem for a vector field $\bf{E}$. For Dirichlet boundary conditions $\bf{n} \times \bf{E} =$ $…
For an arbitrary ordinary second order differential equation a test is constructed that checks if this equation is equivalent to Painleve I, II or Painleve III with three zero parameters equations under the substitutions of variables. If it…
The two matrix model is considered, with measure given by the exponential of a sum of polynomials in two different variables. It is shown how to derive a sequence of pairs of ``dual'' finite size systems of ODEs for the corresponding…
Apparently, all partial differential equations that describe physical phenomena in space-time can be cast into a universal quasilinear, first-order form. In this paper, we do two things. First, we describe some broad features of systems of…
This thesis is divided in two parts. The first part contains the study of some properties of the electromagnetic duality in 4 dimensions. An extended double potential formalism for linearized gravity is introduced which allows to write an…
We discuss duality in ``two-photon''-like processes in the scalar $\varphi^3_E$ model and also in the process $\gamma^*\gamma\to\pi\pi$ in QCD. Duality implies the equivalence between two distinct nonperturbative mechanisms. These two…
In this dissertation we study basic local differential geometry, projective differential geometry, and prolongations of overdetermined geometric partial differential equations. It is simple to prolong an n-th order linear ordinary…
In this paper, we solve certain Fermat-type partial differential-difference equations for finite order entire functions of several complex variables. These results are significant generalizations of some earlier findings, especially those…
Difference equations have many applications and play an important role in numerical analysis, probability, statistics, combinatorics, computer science, quantum consciousness, etc. We first prove that the partial differential equation is…
In this paper we construct the main algebraic and differential properties and the weight functions of orthogonal polynomial solutions of bivariate second--order linear partial differential equations, which are admissible potentially…